Equations of Planes, Coplanarity

Grade 12 Maths Higher — Equations of Planes, Coplanarity: 25 practice questions with instant scoring and explanations.

1. Equation of plane with normal n = (a, b, c) passing through P₀(x₀, y₀, z₀):
2. General equation of plane: ax + by + cz + d = 0. Normal vector is:
3. Plane passing through three points A, B, C has normal:
4. Condition for four points to be coplanar:
5. Vector form of plane: n·(r - a) = 0 means:
6. Intercept form of plane x/a + y/b + z/c = 1 represents:
7. Distance from point P(x₁, y₁, z₁) to plane ax + by + cz + d = 0:
8. Angle θ between planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0:
9. Two planes are parallel if their normals are:
10. Two planes are perpendicular if their normals satisfy:
11. Plane through line of intersection of two planes:
12. Distance between parallel planes ax + by + cz + d₁ = 0 and ax + by + cz + d₂ = 0:
13. Plane 2x + 3y - z = 5 has normal:
14. Point (1, 2, 3) lies on plane x + 2y - z = 2:
15. Planes parallel to xy-plane have form:
16. Foot of perpendicular from P to plane ax + by + cz + d = 0 is found by:
17. Plane through line r = a + tb and point P:
18. Symmetric form of plane equation: (r - a)·n = 0 where n =
19. Four points coplanar condition uses determinant:
20. Projection of point P onto plane:
21. Plane 3x - 2y + 6z = 18 has intercepts on axes:
22. Equation of plane through origin:
23. Bisecting planes of angle between two planes:
24. Planes x - 2y + z = 3 and 2x - 4y + 2z = 5 are:
25. Review question for Equations of Planes, Coplanarity